Question 330255
{{{(x+10)(x-3)(x+5)>0 }}}
Break up the number line into 4 regions.
Region 1:( {{{-infinity}}},{{{-10}}})
Region 2:({{{-10}}},{{{-5}}})
Region 3:({{{-5}}},{{{3}}})
Region 4:({{{3}}}, {{{infinity}}})
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Choose a point (not an endpoint) in the region and test the inequality.
Region 1: {{{x=-11}}}
{{{(x+10)(x-3)(x+5)>0}}}
{{{(-11+10)(-11-3)(-11+5)>0}}}
{{{(-1)(-14)(-6)>0}}}
{{{-84>0}}}
False, this region is not part of the solution.
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Region 2: {{{x=-7}}}
{{{(x+10)(x-3)(x+5)>0}}}
{{{(-7+10)(-7-3)(-7+5)>0}}}
{{{(3)(-10)(-2)>0}}}
{{{60>0}}}
True, this region is part of the solution.
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Region 3: {{{x=0}}}
{{{(x+10)(x-3)(x+5)>0}}}
{{{(10)(-3)(5)>0}}}
{{{-150>0}}}
False, this region is not part of the solution.
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Region 4: {{{x=4}}}
{{{(x+10)(x-3)(x+5)>0}}}
{{{(14)(1)(9)>0}}}
{{{126>0}}}
True, this region is part of the solution.
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({{{-10}}},{{{-5}}}) U ({{{3}}}, {{{infinity}}})
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Graphically look for when the function is above the x-axis.
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{{{drawing(300,300,-15,5,-100,100,blue(line(-10,-100,-10,100)),blue(line(-5,-100,-5,100)),blue(line(3,100,3,-100)),grid(1),graph(300,300,-15,5,-100,100,(x+10)(x-3)(x+5)))}}}